Matrix groups are the most concrete examples of Lie groups. They are fundamental to many diverse fields of Mathematics and Physics. Matrix groups are simultaneously geometric and algebraic objects. Students in this course will therefore have their geometric and algebraic intuition sharpened and challenged as we study topics including: orthogonal groups, matrix exponentiation, topology, maximal tori, Weil groups, and the question of which matrix groups are isomorphic to each other. Format: seminar. Evaluation will be based on homework, classwork, problem sets and exams. Prerequisites: Mathematics 312 or 315, and any one of 301, 305, 321, 323, 324, 326, or permission of instructor. No enrollment limit (expected: 12).